How to Find the Linearization of the Cosine Function at a Given Point

[crybllrd]

Homework Statement

Find the linearization L(x) of f(x) = cos(x) at a = π/2

Homework Equations

L(x) = f(a) + f'(a)(x-a)

The Attempt at a Solution

I just want to make sure I did this correctly:

L(x) = cos(π/2) + -sin(π/2)(x-(π/2))

L(x) = 0-1(x-(π/2))

L(x) = -x + (π/2)

Do I need to substitute something in for x, or is this the answer?

 

[CompuChip]

Looks fine to me.
What you can do is plot f(x) and L(x) in the same graph.
If you did it correctly, the graph of L(x) should touch that of f(x) at x = π/2 and approximate it quite well in a small region around it (after all, that's the whole point of linearization).

 

[crybllrd]

Thanks a lot!